NEW ORLEANS — From the beginning Spike Lee knew that Hurricane Katrina was a story he had to tell. Watching the first television images of floating bodies and of desperate people, mostly black, stranded on rooftops, he quickly realized he was witnessing a major historical moment. As those moments kept coming, he spent almost a year capturing the hurricane’s sorrowful consequences for a four-hour documentary, “When the Levees Broke: A Requiem in Four Acts,” to be shown on HBO this month.